Capcom's Seth Killian has explained why PlayStation 3 Super Street Fighter IV players cannot see the DLC costumes of their opponents unless they've also purchased the DLC, when Xbox 360 gamers can see all costumes regardless of his or her purchases (via Eurogamer).
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The DLC for the newest costumes is additional data that must be put on your machines from the first-party networks (XBL and PSN). When you add new data to an existing product, there are significant costs to do so charged by the first parties. On XBL, those costs were covered by Microsoft. As a result, the data is distributed to everyone, so even if you have not bought the new costumes, you can still see them if you're fighting against someone that has because you still received the new data required to display them.

Sony did not cover these costs, so Capcom would have had to pay to provide the data to users that did not purchase the DLC--likely to many more users than would have purchased the content. That, of course, would have reduced the amount of money made from the DLC, thereby defeating the entire point of DLC for Capcom.